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Register a new userQuantum Bayesianism: A Study
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Christopher Gordon Timpson
Publication date
2008
fields
Physics
and research's language is
English
Authors
Christopher G. Timpson
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The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigners friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwrights philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moores paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments.
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The lately developed part of Quantum Bayesianism named QBism has been proclaimed by its authors a powerful interpretation of Quantum Physics. This article presents analysis of some aspects of QBism. The considered examples show inconsistencies in some basic statements of the discussed interpretation. In particular, the main quantum mechanical conundrum of measurement and the observer is, contrary to the claims, not resolved within the framework of QBism. The conclusion is made that the basic tenets of QBism as applied in Physics are unsubstantiated.
This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing definitions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python statistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo.
Along with the development of AI democratization, the machine learning approach, in particular neural networks, has been applied to wide-range applications. In different application scenarios, the neural network will be accelerated on the tailored computing platform. The acceleration of neural networks on classical computing platforms, such as CPU, GPU, FPGA, ASIC, has been widely studied; however, when the scale of the application consistently grows up, the memory bottleneck becomes obvious, widely known as memory-wall. In response to such a challenge, advanced quantum computing, which can represent 2^N states with N quantum bits (qubits), is regarded as a promising solution. It is imminent to know how to design the quantum circuit for accelerating neural networks. Most recently, there are initial works studying how to map neural networks to actual quantum processors. To better understand the state-of-the-art design and inspire new design methodology, this paper carries out a case study to demonstrate an end-to-end implementation. On the neural network side, we employ the multilayer perceptron to complete image classification tasks using the standard and widely used MNIST dataset. On the quantum computing side, we target IBM Quantum processors, which can be programmed and simulated by using IBM Qiskit. This work targets the acceleration of the inference phase of a trained neural network on the quantum processor. Along with the case study, we will demonstrate the typical procedure for mapping neural networks to quantum circuits.
Measurements on classical systems are usually idealized and assumed to have infinite precision. In practice, however, any measurement has a finite resolution. We investigate the theory of non-ideal measurements in classical mechanics using a measurement probe with finite resolution. We use the von Neumann interaction model to represent the interaction between system and probe. We find that in reality classical systems are affected by measurement in a similar manner as quantum systems. In particular, we derive classical equivalents of Luders rule, the collapse postulate, and the Lindblad equation.
Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network constructed by quantum gate. In this model, we mapped the feature data to a quantum state in Hilbert space firstly, and then implement unitary evolution on it, in the end, we can get the classification result by im-plement measurement on the quantum state. Since all the operations in quan-tum neural networks are unitary, the parameters constitute a hypersphere of Hilbert space. Compared with traditional neural network, the parameter space is flatter. Therefore, it is not easy to fall into local optimum, which means the quantum neural networks have better generalization. In order to validate our proposal, we evaluated our model on three public datasets, the results demonstrated that our model has better generalization than the classical neu-ral network with the same structure.
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